Problem: Simplify the following expression: $\dfrac{12z^2}{72z^5}$ You can assume $z \neq 0$.
Answer: $ \dfrac{12z^2}{72z^5} = \dfrac{12}{72} \cdot \dfrac{z^2}{z^5} $ To simplify $\frac{12}{72}$ , find the greatest common factor (GCD) of $12$ and $72$ $12 = 2 \cdot 2 \cdot 3$ $72 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(12, 72) = 2 \cdot 2 \cdot 3 = 12 $ $ \dfrac{12}{72} \cdot \dfrac{z^2}{z^5} = \dfrac{12 \cdot 1}{12 \cdot 6} \cdot \dfrac{z^2}{z^5} $ $\phantom{ \dfrac{12}{72} \cdot \dfrac{2}{5}} = \dfrac{1}{6} \cdot \dfrac{z^2}{z^5} $ $ \dfrac{z^2}{z^5} = \dfrac{z \cdot z}{z \cdot z \cdot z \cdot z \cdot z} = \dfrac{1}{z^3} $ $ \dfrac{1}{6} \cdot \dfrac{1}{z^3} = \dfrac{1}{6z^3} $